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A342666 a(n) = A336466(A156552(n)).

%I A342666 #9 Jan 29 2022 20:15:03
%S A342666 1,1,1,1,1,1,3,1,1,1,5,1,1,1,1,1,3,1,9,1,5,1,11,1,3,3,3,1,3,1,15,1,21,
%T A342666 1,1,1,1,5,3,1,9,1,33,5,9,1,23,1,1,3,65,1,7,1,35,21,5,1,21,1,341,9,3,
%U A342666 1,11,1,27,1,5,1,5,1,15,3,51,1,27,1,39,1,1365,1,1,5,49,9,1,1,1,1,117,5,825,3,9,1,9,3,1,1,7,1
%N A342666 a(n) = A336466(A156552(n)).
%H A342666 Antti Karttunen, <a href="/A342666/b342666.txt">Table of n, a(n) for n = 2..10000</a> (based on Hans Havermann's factorization of A156552)
%H A342666 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A342666 a(n) = A336466(A156552(n)) = A336466(A322993(n)).
%F A342666 a(p) = 1 for all primes p.
%F A342666 a(A003961(n)) = a(n).
%o A342666 (PARI)
%o A342666 A000265(n) = (n>>valuation(n,2));
%o A342666 A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };
%o A342666 A156552(n) = {my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res};
%o A342666 A342666(n) = A336466(A156552(n));
%o A342666 (PARI)
%o A342666 \\ Version using the factorization file available at https://oeis.org/A156552/a156552.txt
%o A342666 v156552sigs = readvec("a156552.txt");
%o A342666 A000265(n) = (n>>valuation(n,2));
%o A342666 A342666(n) = if(isprime(n),1,my(prsig=v156552sigs[n],ps=prsig[1],es=prsig[2]); prod(i=1,#ps,A000265(ps[i]-1)^es[i])); \\ _Antti Karttunen_, Jan 29 2022
%Y A342666 Cf. A000265, A003961, A156552, A322993, A336466.
%Y A342666 Cf. also A324104, A342651, A342656, A350067.
%K A342666 nonn
%O A342666 2,7
%A A342666 _Antti Karttunen_, Mar 18 2021